One of the most interesting subjects taught in middle and high school is Statistics. This subject originated from mathematics and holds the utmost importance in this era of data science. In Statistics, students learn how to collect, analyze, interpret and present data. In this article, we will learn what frequency distribution in statistics is and how we can make a Frequency Distribution Table.
What is Frequency?
The statistical data can comprise various numbers. These numbers might be completely unique or repeat more than one time in the data. The number of times any number repeats in a statistical data is called its Frequency.
Example: A newspaper shop has sold the following numbers of newspapers in 12 days –
10, 12, 5, 10, 7, 20, 11, 10, 3, 10, 12, 7
The frequency of the number of newspapers sold in 12 days will be –
(Number of newspapers sold)
From the table above, we can see that the frequency of 3 newspapers is 1. This means 3 newspapers were sold on only 1 day. Similarly, the frequency of 10 is 4. This means that there were total 4 days on which 10 newspapers were sold.
What is the Frequency Distribution Table?
When we list the corresponding frequencies of the items in a statistical data set in the form of a table, it is called Frequency Distribution Table. The list of frequencies and the corresponding data items are called Frequency Distribution.
The table given in the above example is a simple or ungrouped frequency distribution table and the list of frequencies corresponding to the number of papers sold is simple or ungrouped frequency distribution. Let us see other types of frequency distribution tables.
Types of Frequency Distributions
Grouped Frequency Distribution
We have seen how data frequencies of data items are determined. In the above example, the number of data items were only 12. What if we have 100 or 1000 data items? It will become very difficult for us to find the frequency corresponding to each data item. To make our frequency distribution calculations easier, we divide the data items into different groups or class intervals. Such a frequency distribution table is called Grouped Frequency Distribution Table.
Example: Data Items – 9,16,13,7,8,4,18,10,17,18,9,12,5,9,9,16,1,8,17,1,10,5,9,11,15,6,14,9,1,12,5,16,4,16,8,15,14,17
To form groups of data items we will first arrange the data in increasing order –
Smallest value = 1
Highest Value = 18
Difference = 17
Now, divide this difference by the number of groups that you desire. Let us say we want 5 groups. Then,
17/5 = 3.4 (Rounded off to 4)
This means that the group size will be 4. Hence the groups will be –
0-3, 4-7, 8-11, 12-15, 16-19
Now the frequency distribution table will be –
Relative Frequency Distribution
The relative frequency of a data item is calculated by dividing the frequency of that data item by the total frequency of the data set. Hence we can say that relative frequency is the portion of the total frequency that belongs to a particular class interval.
A frequency distribution table in which the frequencies of data items are the respective relative frequencies is called the Relative Frequency Distribution Table.
Example: Consider the example given above, where the total of all frequencies is 38.
Relative Frequency = f/n
Where f = the frequency of the data item
n = total of frequencies of the complete data set
So, the relative frequency table for the class intervals mentioned in the above example will be –
|Data Groups||Frequency||Relative Frequency|
|0-3 cm||3||3/38 = 0.078|
|4-7 cm||7||7/38 = 0.184|
|8-11 cm||12||12/38 = 0.315|
|12-15 cm||7||7/38 = 0.184|
|16-19 cm||9||9/38 = 0.236|
Cumulative Frequency Distribution
When the frequency distribution of a class is the sum of its frequency and that of the classes below it, it is called Cumulative Frequency Distribution. A frequency distribution table that represents cumulative frequencies is called the Cumulative Frequency Distribution Table. This type of frequency distribution is useful when we want to measure frequency up to a certain limit or threshold.
Example: Consider the frequency distribution table,
Cumulative Frequency table would be,
Relative Cumulative Frequency Distribution
When the cumulative frequencies are divided by the total frequency, we obtain relative cumulative frequencies. When we create a frequency distribution table of these frequencies, it is called the Relative Cumulative Frequency Distribution Table.
Consider the cumulative frequency distribution given below,
Here, total frequency = 38
So the relative cumulative frequency distribution would be,
|Data Groups||Frequency||Relative Cumulative Frequency|
|0-3 cm||3||3/38 = 0.078|
|4-7 cm||10||10/38 = 0.263|
|8-11 cm||22||22/38 = 0.579|
|12-15 cm||29||29/38 = 0.763|
|16-19 cm||38||38/38 = 1|
With this, we have learned how to create an ungrouped, grouped, relative, cumulative, relative cumulative frequency tables. Are you ready to strike off that frequency distribution table assignment from your to-do list? Not yet? Then, seek dissertation help from GoDissertationhelp! Our statistics experts will provide you with accurate solutions and correct explanations for your assignment questions. If you are working on a statistics paper, our experts can provide you with complete assignment assistance. Connect with us today to know more about our dissertation writing services and exclusive offers.